Particle-in-wavelets scheme for the 1D Vlasov-Poisson equations

A new numerical scheme called particle-in-wavelets is proposed for the Vlasov-Poisson equations, and tested in the simplest case of one spatial dimension. The plasma distribution function is discretized using tracer particles, and the charge distribution is reconstructed using wavelet-based density estimation. The latter consists in projecting the Delta distributions corresponding to the particles onto a finite dimensional linear space spanned by a family of wavelets, which is chosen adaptively. The stability and accuracy of the scheme is supported by numerical computations of Landau damping and of the two-stream instability. By direct comparison with a reference solution obtained by a very precise semi-Lagrangian method, we show that the precision is improved roughly by a factor 3 compared to a classical PIC scheme, for a given number of particles.